Localization plays an important role in robotics for the tasks of monitoring, tracking and controlling a robot. Much effort has been made to address robot localization problems in recent years. However, despite many proposed solutions and thorough consideration, in terms of developing a low-cost and fast processing method for multiple-source signals, the robot localization problem is still a challenge. In this paper, we propose a solution for robot localization with regards to these concerns. In order to locate the position of a robot, both the coordinate and the orientation of a robot are necessary. We develop a localization method using the Matrix Pencil (MP) algorithm for hybrid detection of direction of arrival (DOA) and time of arrival (TOA). TOA of the signal is estimated for computing the distance between the mobile robot and a base station (BS). Based on the distance and the estimated DOA, we can estimate the mobile robot's position. The characteristics of the algorithm are examined through analysing simulated experiments and the results demonstrate the advantages of our method over previous works in dealing with the above challenges. The method is constructed based on the low-cost infrastructure of radio frequency devices; the DOA/TOA estimation is performed with just single value decomposition for fast processing. Finally, the MP algorithm combined with tracking using a Kalman filter allows our proposed method to locate the positions of multiple source signals.